Invalidate widget output cache when updating posts, categories, terms, menus, etc.

widget-cache-bump.php

<?php

add_action( 'init', 'widget_cache_register_bump' );

function widget_cache_register_bump() {

	// Invalidate widget cache during these action calls
	$purge_actions = array(
		'clean_post_cache',
		'edit_term',
		'publish_post',
		'comment_post',
		'delete_comment',
		'edit_comment',
		'delete_post',
		'edit_post',
		'wp_update_nav_menu',
		'activated_plugin',
		'deactivated_plugin',
		'wp_maybe_auto_update'
	);

	foreach ( $purge_actions as $action ) {
		add_action( $action, 'widget_cache_do_bump' );
	}

}

function widget_cache_do_bump() {
	update_option( 'cache-widgets-version', time() );
}